The soda farl sandwich is named for its bread, and the farl is the soda dough cooked a different way: not baked into a loaf but griddled flat into a soft quarter round. A round of soda dough is cut into four triangular farls and cooked on a hot griddle or pan rather than in the oven, which gives it a soft, pale, floury surface, a tender close crumb, and no hard caramelised crust at all. Split through its thickness and filled, it is the everyday bread of the Ulster fry, and the defining fact is that it is griddled, not baked: that single change of method makes it softer, flatter, and quicker to stale than the soda loaf it is otherwise the same dough as, and the sandwich is built around that softness.
The craft follows from what a griddled farl does. It is at its best within hours of cooking, soft and pliable while warm and going leathery and dry once it cools, so it is filled and eaten the same day, often warmed or fried again on the cut side before the filling goes in. Fried in bacon fat, the cut face takes colour and salt and firms just enough to hold a wet fry-up filling without going to paste, which is why it is treated on the pan rather than buttered cold. The crumb has little structural give next to a soft roll, so the farl works as a flat carrier for a hot, fatty filling rather than a yielding cushion around it, and a runny yolk earns its place by supplying the lubrication a buttered roll would otherwise carry. It is eaten hot off the griddle because there is no waterproofed crumb to hold it once it sits.
The variations are the rest of the Ulster fry it is cut from and the griddle breads that parallel it. The farl with bacon and egg is the construction named for its filling; potato bread, or fadge, is the other Northern Irish griddle base for the identical fry-up; the soda loaf is the same dough baked rather than griddled, sturdier and longer-keeping. Each deserves its own article rather than being crowded in here.